A057327 -id:A057327 - cp's OEIS frontend

A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)).

2, 3, 7, 19, 31, 37, 79, 97, 99, 135, 139, 157, 198, 199, 211, 229, 271, 287, 307, 331, 337, 350, 367, 379, 439, 499, 539, 547, 577, 601, 607, 619, 661, 671, 691, 727, 811, 829, 877, 923, 937, 967, 997, 1009, 1069, 1171, 1237, 1254, 1279, 1297, 1399, 1429

Offset: 1

Michel Lagneau, Mar 22 2010

nonn

A005382 is included in this sequence : if p and 2p-1 primes, phi(p) = p-1, sigma(p)=p+1 and sigma(2p-1)=2p => phi(p) +sigma(p) = sigma(p+phi(p)). See the similar sequence A005384.

			2 is in the sequence because phi(2) + sigma(2) = 1 + 3 = 4, and sigma(2 + phi(2)) = sigma(3) = 4;
99 is in the sequence because phi(99) + sigma(99) = 60 + 156 = 216, and sigma(99 + phi(99)) = sigma(159) = 216.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

Amiram Eldar, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Cf. A005382, A005384, A057326, A057327, A057328, A057330, A005603.

[n: n in [1..1500] | (EulerPhi(n) + SumOfDivisors(n)) eq (SumOfDivisors(n + EulerPhi(n)))]; // Vincenzo Librandi, Jul 15 2015

with(numtheory):for n from 1 to 3000 do :if phi(n)+sigma(n) = sigma(n+phi(n)) then print(n):else fi:od:

Select[Range[1500],EulerPhi[#]+DivisorSigma[1,#]==DivisorSigma[1, #+ EulerPhi[ #]]&] (* Harvey P. Dale, Jul 05 2018 *)

A289109 Primes p that remain prime through 3 iterations of function f(x) = 6x - 1.

Original entry on oeis.org

239, 269, 439, 569, 599, 829, 1429, 3389, 6379, 7159, 7649, 8779, 8969, 10799, 10939, 12919, 13729, 13879, 15649, 17159, 18149, 19379, 21649, 22669, 23929, 24799, 25679, 26849, 28219, 30389, 30689, 33749, 34759, 36109, 36209, 36899, 40759, 47659, 49639, 52369

Offset: 1

K. D. Bajpai, Jun 24 2017

nonn

All the terms are congruent to 9 (mod 10). The iteration of f(x) on a term of this sequence then produces primes congruent to 3, 7, 1 (mod 10), followed by a nontrivial multiple of 5.

			239 is prime and 6 * 239 - 1 = 1433, which is also prime. 6 * 1433 - 1 = 8597, which is also prime. 6 * 8597 = 51581, which is also prime. 6 * 51581 - 1 = 309485 = 5 * 11 * 17 * 331, which is composite, but the previous three primes are enough for 239 to be in the sequence.
241 is not in the sequence because 6 * 241 - 1 = 1445 = 5 * 17^2, which is composite.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A057326, A057327, A057328, A057329, A057330, A158015.

filter:= x -> andmap(isprime, [x,6*x-1,36*x-7,216*x-43]):
select(filter, [seq(i,i=9..60000,10)]); # Robert Israel, May 10 2020

Select[Prime[Range[15000]], And @@ PrimeQ[NestList[6 # - 1 &, #, 3]] &]

forprime(p= 1, 100000, if(isprime(6*p-1) && isprime(36*p-7) && isprime(216*p-43) , print1(p, ", ")));

cp's OEIS Frontend

A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)).

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